共查询到20条相似文献,搜索用时 28 毫秒
1.
Saroj Kumar Dash 《Journal of Mathematical Analysis and Applications》2008,339(1):98-107
For a symmetric stable process X(t,ω) with index α∈(1,2], f∈Lp[0,2π], p?α, and , we establish that the random Fourier-Stieltjes (RFS) series converges in the mean to the stochastic integral , where fβ is the fractional integral of order β of the function f for . Further it is proved that the RFS series is Abel summable to . Also we define fractional derivative of the sum of order β for an, An(ω) as above and . We have shown that the formal fractional derivative of the series of order β exists in the sense of mean. 相似文献
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Let be the polynomial whose zeros are the j-invariants of supersingular elliptic curves over . Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier (Computational Perspectives on Number Theory (Chicago, IL, 1995), AMS/IP 7 (1998) 97-126), we define an inner product on for every . Suppose a system of orthogonal polynomials {Pn,ψ(x)}n=0∞ with respect to exists. We prove that if n is sufficiently large and ψ(x)Pn,ψ(x) is p-integral, then over . Further, we obtain an interpretation of these orthogonal polynomials as a p-adic limit of polynomials associated to p-adic modular forms. 相似文献
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Tomoyoshi Ohwada Guoxing Ji Atsushi Hasegawa 《Journal of Mathematical Analysis and Applications》2006,315(1):216-224
Let G be a compact abelian group with the totally ordered dual group which admits the positive semigroup . Let N be a von Neumann algebra and be an automorphism group of on N. We denote to the analytic crossed product determined by N and α. We show that if is a maximal σ-weakly closed subalgebra of , then induces an archimedean order in . 相似文献
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Giuseppe Zampieri 《Journal of Mathematical Analysis and Applications》2003,283(1):150-158
Let be a CR mapping between real analytic generic submanifolds M, M1 of and , respectively. According to Webster's theory (Proc. Amer. Math. Soc. 86 (1982) 236-240) and its further developments, f has holomorphic extension to a full neighborhood of M in when the following requirements are fulfilled: f extends to a wedge W continuous up to M; f is of class Ck; (where denotes the complex tangent bundle); M1 is “k-nondegenerate.” We deal here with the case where is strictly smaller than but is still real analytic in suitable sense. We show that a suitably refined condition of k-nondegeneracy still entails holomorphic extension of f. 相似文献
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Emin Özça? ?nci Ege Ha?met Gürçay 《Journal of Mathematical Analysis and Applications》2007,326(1):101-107
The distributions and were defined as the neutrix limit of the sequences and respectively for , see [J.D. Nicholos, B. Fisher, The distribution composition , J. Math. Anal. Appl. 258 (2001) 131-145; B. Fisher, On defining the distribution , Univ. u Novom Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 15 (1985) 119-129]. We here consider these distributions when r=0. In other words, we define the sth powers of the Heaviside function H(x) in the distributional sense for negative integers. Further compositions are also considered. 相似文献
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Let , B and Aj () be real nonsingular n×n matrices, λk () be real numbers. In this paper we present a sufficient condition for the system to be a frame for . This sufficient condition also shows the stability of the system with respect to the perturbation of matrix dilation parameters and the perturbation of translation parameters . 相似文献
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Let C be a closed convex subset of a uniformly smooth Banach space E and let T:C→C be a nonexpansive mapping with a nonempty fixed points set. Given a point u∈C, the initial guess x0∈C is chosen arbitrarily and given sequences , and in (0,1), the following conditions are satisfied:
- (i)
- ;
- (ii)
- αn→0, βn→0 and 0<a?γn, for some a∈(0,1);
- (iii)
- , and . Let be a composite iteration process defined by
11.
Feng Dai 《Journal of Mathematical Analysis and Applications》2006,315(2):711-724
We study the Kolmogorov m-widths and the linear m-widths of the weighted Besov classes on [−1,1], where Lq,μ, 1?q?∞, denotes the Lq space on [−1,1] with respect to the measure , μ>0. Optimal asymptotic orders of and as m→∞ are obtained for all 1?p,τ?∞. It turns out that in many cases, the orders of are significantly smaller than the corresponding orders of the best m-term approximation by ultraspherical polynomials, which is somewhat surprising. 相似文献
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On commutators of Marcinkiewicz integrals with rough kernel 总被引:2,自引:0,他引:2
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Schwartz's almost periodic distributions are generalized to the case of Banach space valued distributions , and furthermore for a given arbitrary class A to for φ∈ test functions D(R,C)}. It is shown that this extension process is iteration complete, i.e. . Moreover the T from are characterized in various ways, also tempered distributions with P={X-valued functions of polynomial growth} are shown. Under suitable assumptions , , where for all h>0}, is defined with the corresponding extension of Mh. With an extension of the indefinite integral from to D′(R,X) a distribution analogue to the Bohl-Bohr-Amerio-Kadets theorem on the almost periodicity of bounded indefinite integrals of almost periodic functions is obtained, also for almost automorphic, Levitan almost periodic and recurrent functions, similar for a result of Levitan concerning ergodic indefinite integrals. For many of the above results a new (Δ)-condition is needed, we show that it holds for most of the A needed in applications. Also an application to the study of asymptotic behavior of distribution solutions of neutral integro-differential-difference systems is given. 相似文献
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Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,308(2):532-540
By constructing the comparison functions and the perturbed method, it is showed that any solution u∈C2(Ω) to the semilinear elliptic problems Δu=k(x)g(u), x∈Ω, u|∂Ω=+∞ satisfies , where Ω is a bounded domain with smooth boundary in RN; , −2<σ, c0>0, ; g∈C1[0,∞), g?0 and is increasing on (0,∞), there exists ρ>0 such that , ∀ξ>0, , . 相似文献
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Tian-Xiao Pang Zheng-Yan Lin 《Journal of Mathematical Analysis and Applications》2007,334(2):1246-1259
Let be a sequence of independent and identically distributed positive random variables, which is in the domain of attraction of the normal law, and tn be a positive, integer random variable. Denote , , where denotes the sample mean. Then we show that the self-normalized random product of the partial sums, , is still asymptotically lognormal under a suitable condition about tn. 相似文献
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